Question: Multiply the following complex numbers: $({4-5i}) \cdot ({-3-5i})$
Solution: Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({4-5i}) \cdot ({-3-5i}) = $ $ ({4} \cdot {-3}) + ({4} \cdot {-5}i) + ({-5}i \cdot {-3}) + ({-5}i \cdot {-5}i) $ Then simplify the terms: $ (-12) + (-20i) + (15i) + (25 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ -12 + (-20 + 15)i + 25i^2 $ After we plug in $i^2 = -1$ , the result becomes $ -12 + (-20 + 15)i - 25 $ The result is simplified: $ (-12 - 25) + (-5i) = -37-5i $